Is there any evidence that in cases that where neither "outside view" nor "strong inside view" can be applied, "weak inside view" is at least considerably better than pure chance? I have strong doubts about it.
Yes, it would be good to have a clearer data set of topics at dates, the views suggested by different styles of analysis, and what we think now about who was right. I'm pretty skeptical about this weak inside view claim, but will defer to some more systematic data. Of course that is my suggesting we take an outside view to evaluating this claim about which view is more reliable.
I really liked Robin's point that mainstream scientists are usually right, while contrarians are usually wrong. We don't need to get into details of the dispute - and usually we cannot really make an informed judgment without spending too much time anyway - just figuring out who's "mainstream" lets us know who's right with high probability. It's type of thinking related to reference class forecasting - find a reference class of similar situations with known outcomes, and we get a pretty decent probability distribution over possible outcomes.
Unfortunately deciding what's the proper reference class is not straightforward, and can be a point of contention. If you put climate change scientists in the reference class of "mainstream science", it gives great credence to their findings. People who doubt them can be freely disbelieved, and any arguments can be dismissed by low success rate of contrarianism against mainstream science.
But, if you put climate change scientists in reference class of "highly politicized science", then the chance of them being completely wrong becomes orders of magnitude higher. We have plenty of examples where such science was completely wrong and persisted in being wrong in spite of overwhelming evidence, as with race and IQ, nuclear winter, and pretty much everything in macroeconomics. Chances of mainstream being right, and contrarians being right are not too dissimilar in such cases.
Or, if the reference class is "science-y Doomsday predictors", then they're almost certainly completely wrong. See Paul Ehrlich (overpopulation), and Matt Simmons (peak oil) for some examples, both treated extremely seriously by mainstream media at time. So far in spite of countless cases of science predicting doom and gloom, not a single one of them turned out to be true, usually not just barely enough to be discounted by anthropic principle, but spectacularly so. Cornucopians were virtually always right.
It's also possible to use multiple reference classes - to view impact on climate according to "highly politicized science" reference class, and impact on human well-being according to "science-y Doomsday predictors" reference class, what's more or less how I think about it.
I'm sure if you thought hard enough, you could come up with other plausible reference classes, each leading to any conclusion you desire. I don't see how one of these reference class reasonings is obviously more valid than others, nor do I see any clear criteria for choosing the right reference class. It seems as subjective as Bayesian priors, except we know in advance we won't have evidence necessary for our views to converge.
The problem doesn't arise only if you agree to reference classes in advance, as you can reasonably do with the original application of forecasting costs of public projects. Does it kill reference class forecasting as a general technique, or is there a way to save it?